Note that the distinction between full and partial Procrustes is not very important if shape variation is in fact very small.
In a partial Procrustes superimposition there is an additional step that projects the aligned specimens onto the tangent space. Without that step the shapes are still in the curved space of GPA aligned shapes. As a result, there will be one less eigenvalue than expected that is “exactly” equal to zero (i.e., around 10^-16). Its size depends on the amount of curvature of the space around the GPA consensus shape and that depends on the amount of shape variation in the sample and thus is data dependent. However, it seems reasonable to me to apply this extra step if one is going to use multivariate methods that assume that one has a linear space. This was discussed in Rohlf, F. J. 1999. Shape statistics: Procrustes superimpositions and tangent spaces. Journal of Classification, 16:197-223. Slice 2001. Syst. Biol. 50:141–149 is also relevant. _ _ _ _ _ _ _ _ _ F. James Rohlf, Distinguished Prof. Emeritus Depts. of Anthropology and of Ecology & Evolution From: Mike Collyer [mailto:mlcoll...@gmail.com] Sent: Tuesday, October 31, 2017 12:29 PM To: andrea cardini <alcard...@gmail.com> Cc: morphmet@morphometrics.org Subject: Re: [MORPHMET] Procrustes fit Andrea, I think it is worth it to do a pedantic review of your exercise for the benefit of the community. First, the differences are not data dependent - they are method dependent. TPSRelw uses partial Procrustes; MorphoJ uses full Procrustes superimposition. PCA would have the exact same variance explained by dimensions (rounding notwithstanding) if the two programs used the same superimposition method. The results are similar because the methods are similar. Maybe what you meant by “data dependent” is that in another case, the different methods might lead to more disparate results, for which I agree. Again, for the benefit of others, I think this distinction is important. Second, I think the special characters had very little to do with the results from the analysis but might indeed cause problems for one program compared to another. This would have more to do with each program’s programming to identify and deal with such things. Cheers! Mike On Oct 31, 2017, at 12:05 PM, andrea cardini <alcard...@gmail.com <mailto:alcard...@gmail.com> > wrote: Dear All, yes, there are differences and they're data dependent but in Andrey's case (as it's my experience all the times I checked with my own data) they're very small. I gave a very quick look and it's better to check more carefully. However, in the screenshot one can see the % of variance explained computed in PAST 2.17, MorphoJ and TPSRelw: they're almost identical and PC1 vs PC2 in the three programs (not shown) look the same except for flipping one or the other axis. The issue may have something to do with special characters in the TPS file: I could run it in TPSRelw only after converting to NTS, which removed the special characters in the image names. Cheers Andrea On 31/10/17 16:35, Adams, Dean [EEOBS] wrote: Andrey, To repeat: there is no reason to expect the numbers to match identically across software packages, particularly column by column (if that is what you are examining). Even if two packages perform things identically in terms of the algebra (e.g,. GPA using TpsRelw and geomorph), the numbers may differ slightly for other reasons (post-rotation of the alignment to the principal axes of the consensus, etc.). What is important for downstream statistical analyses is not the individual columns of numbers found from the GPA alignment, but rather the relationships of specimens in the resultant shape space. That is, how different are shapes from one another? In the case I mentioned above, if you took the aligned specimens from TpsRelw and obtained the Procrustes (Euclidean) distance matrix from them, and did the same with the aligned specimens from geomorph, and then performed a matrix correlation, the correlation would be precisely 1.0. This means the information is identical in the two superimpositions, even if they differ slightly in how the entire set is oriented relative to the X-Y axis. Incidentally, in the above case one would also find a perfect correlation between distances from the GPA-aligned specimens, those shapes rotated to their principal axes, or differences in shape found from the thin-plate spline and uniform shape components taken together. For an early discussion of these issues see Rohlf 1999. However, performing the procedure above where one set of GPA-aligned coordinates is from MorphoJ will not produce a perfect correlation of 1.0, as MorphoJ uses Full Procrustes superimposition. That means the perceived relationships between shapes is not being represented in the same manner: which of course is a known difference between full and partial Procrustes fitting. How much of a difference one finds between a full and partial Procrustes alignment is dataset dependent. Dean Dr. Dean C. Adams Professor Department of Ecology, Evolution, and Organismal Biology Department of Statistics Iowa State University www.public.iastate.edu/~dcadams <http://www.public.iastate.edu/~dcadams> /<http://www.public.iastate.edu/~dcadams/> phone: 515-294-3834 *From:*Andrey Lissovsky [mailto:andlis...@gmail.com] *Sent:* Tuesday, October 31, 2017 10:21 AM *To:* MORPHMET <morphmet@morphometrics.org <mailto:morphmet@morphometrics.org> > *Cc:* andlis...@gmail.com <mailto:andlis...@gmail.com> ; volk...@yandex.ru <mailto:volk...@yandex.ru> *Subject:* Re: [MORPHMET] Procrustes fit Thank you Dean, Of course, numbers should differ. But in my case, there is no correlation between two sets. I guess that in theory the two sets should have r at least around 0.9? On Tuesday, October 31, 2017 at 5:31:51 PM UTC+3, dcadams wrote: Andrey, It is unreasonable to expect the numbers will match perfectly between these two software packages, as the way in which they perform the operations differs. First, MorphoJ uses Full Procrustes fit, whereas the TPS series, geomorph, and others use Partial Procrustes fitting. That will make a difference. Second, there may be additional differences in in how the superimponsed specimens, and thus the consensus, is aligned relative to the X-Y coordinate system. Some packages allow one to rotate the consensus and aligned specimens to their principal axes post-superimposition. That too could lead to differences. Dean Dr. Dean C. Adams Professor Department of Ecology, Evolution, and Organismal Biology Department of Statistics Iowa State University www.public.iastate.edu/~dcadams/ <http://www.public.iastate.edu/~dcadams/> <http://www.public.iastate.edu/~dcadams/> phone: 515-294-3834 *From:*Andrey Lissovsky [mailto:andl...@gmail.com <http://gmail.com/> <javascript:>] *Sent:* Tuesday, October 31, 2017 9:26 AM *To:* MORPHMET <morp...@morphometrics.org <http://morphometrics.org/> <javascript:>> *Cc:* andl...@gmail.com <http://gmail.com/> <javascript:>; vol...@yandex.ru <http://yandex.ru/> <javascript:> *Subject:* Re: [MORPHMET] Procrustes fit Thank you, Andrea I understand that difference should be tiny, so something goes wrong. I enclose one of my tps files. Usually I check dots and commas, so the reason is probably in some different way.. It is possible that I am mixing up menu items.. Last time I use this software, the labels were different. Now I use: In MorphoJ: Preliminaries -- New Procrustes fit -- Align by principle axes then: Export dataset -- Procrustes coordinates In TPS Relw: Actions -- Consensus then: File -- Save -- Aligned specimens Is this ok? Should these chains lead to the same results? On Tuesday, October 31, 2017 at 5:04:56 PM UTC+3, alcardini wrote: Andrey, the last time I checked this (last July, I believe), differences between MorphoJ and TPSRelw were tiny and negligible. I compared MorphoJ with R in the last days, and again differences were tiny. The first thing I'd check is whether there's an issue with commas vs dots as decimal separators. If you send me the tps file, I can give a quick look. Cheers Andrea -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org <http://www.morphometrics.org/> --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+u...@morphometrics.org <http://morphometrics.org/> <javascript:>. -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org <http://www.morphometrics.org/> --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org <mailto:morphmet+unsubscr...@morphometrics.org> <mailto:morphmet+unsubscr...@morphometrics.org>. -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org <http://www.morphometrics.org/> --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org <mailto:morphmet+unsubscr...@morphometrics.org> <mailto:morphmet+unsubscr...@morphometrics.org>. -- Dr. Andrea Cardini Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy tel. 0039 059 2058472 Adjunct Associate Professor, School of Anatomy, Physiology and Human Biology, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia E-mail address: <mailto:alcard...@gmail.com> alcard...@gmail.com, <mailto:andrea.card...@unimore.it> andrea.card...@unimore.it WEBPAGE: <https://sites.google.com/site/alcardini/home/main> https://sites.google.com/site/alcardini/home/main FREE Yellow BOOK on Geometric Morphometrics: <http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf> http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf ESTIMATE YOUR GLOBAL FOOTPRINT: <http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/> http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ -- MORPHMET may be accessed via its webpage at <http://www.morphometrics.org/> http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to <mailto:morphmet+unsubscr...@morphometrics.org> morphmet+unsubscr...@morphometrics.org. <Selection_004.jpg> -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org <mailto:morphmet+unsubscr...@morphometrics.org> . -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.
